Algebra 2 Problems of the Day

Daily Algebra 2 questions and answers.

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June 2017, Part I

All Questions in Part I are worth 2 credits. No work need be shown. No partial credit.


7. The solution to the equation 4x² + 98 = 0 is
1) + 7
2) + 7i
3) + 7*SQRT(2)/2
4) + 7i*SQRT(2)/2

Answer: 4) + 7i*SQRT(2)/2
This isn't the difference of squares. It has a sum, so when we move it to the other side of the equation, you have to take the square root of a negative number. That means an i in the answer.

4x² + 98 = 0
4x² = -98
x² = -98/4
x² = (-1)(2)(49)/(4)
x = +SQRT((-1)(2)(49)/(4))
x = + 7i*SQRT(2)/2

8. Which equation is represented by the graph shown below?

1) y = 1/2 cos 2x
2) y = cos x
3) y = 1/2 cos x
4) y = 2 cos 1/2x

Answer: 1) y = 1/2 cos 2x
At x = 0, the graph is at 0.5, or 1/2, so this eliminates choices 2 and 4, which would have amplitudes of 1 and 2, respectively. The cycle repeats at 1 pi, instead of 2 pi, so the answer is choice 1.

9. A manufacturing company has developed a cost model, C(x) = 0.15x³ + 0.01x² + 2x + 120, where x is the number of items sold, in thousands. The sales price can be modeled by S(x) = 30 − 0.01x. Therefore, revenue is modeled by R(x) = x • S(x). The company's profit, P(x) = R(x) − C(x), could be modeled by
1) 0.15x³ + 0.02x² - 28x + 120
2) -0.15x³ - 0.02x² + 28x - 120
3) -0.15x³ + 0.01x² - 2.01x - 120
4) -0.15x³ + 32x + 120

Answer: 2) -0.15x³ - 0.02x² + 28x - 120
Substitute. Multiply. Combine like terms.
P(x) = R(x) − C(x)
P(x) = x • S(x) − C(x)
P(x) = x (30 − 0.01x) - (0.15x³ + 0.01x² + 2x + 120)
P(x) = 30x − 0.01x² - 0.15x³ - 0.01x² - 2x - 120
P(x) = - 0.15x³ − 0.01x² - 0.01x² + 30x - 2x - 120
P(x) = - 0.15x³ − 0.02x² + 28x - 120

Comments and questions welcome.

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